// modelMatrix is passed by reference for efficiency only. It is not modified.
private static void TransformSingular(ref Matrix3D modelMatrix,
ref Point3D origin, ref Vector3D direction)
{
double [,] matrix = TransformedLineMatrix(ref modelMatrix, ref origin, ref direction);
matrix = Square(matrix);
double[,] eigen = new double[, ] {
{ 1, 0, 0, 0 }, { 0, 1, 0, 0 }, { 0, 0, 1, 0 }, { 0, 0, 0, 1 }
};
// We'll just do 5 iterations with each pair because according to my results & Golub &
// Van Loan this process converges quickly.
int iterations = 5 * s_pairsCount;
for (int iter = 0; iter < iterations; ++iter)
{
int pair = iter % s_pairsCount;
JacobiRotation jrot = new JacobiRotation(s_pairs[pair, 0], s_pairs[pair, 1], matrix);
matrix = jrot.LeftRightMultiply(matrix);
eigen = jrot.RightMultiply(eigen);
}
// That was it as far as finding eigenvectors
int evec1, evec2;
FindSmallestTwoDiagonal(matrix, out evec1, out evec2);
// The eigenvectors corresponding to the two smallest eigenvalues are columns evec1 &
// evec2. These, in homogeneous space, are two different points on our line. We are
// going to convert them to an affine point & vector.
ColumnsToAffinePointVector(eigen, evec1, evec2, out origin, out direction);
}
// modelMatrix is passed by reference for efficiency only. It is not modified.
private static void TransformSingular(ref Matrix3D modelMatrix,
ref Point3D origin, ref Vector3D direction)
{
double [,] matrix = TransformedLineMatrix(ref modelMatrix, ref origin, ref direction);
matrix = Square(matrix);
double[,] eigen = new double[,]{ {1,0,0,0}, {0,1,0,0}, {0,0,1,0}, {0,0,0,1} };
// We'll just do 5 iterations with each pair because according to my results & Golub &
// Van Loan this process converges quickly.
int iterations = 5 * s_pairsCount;
for (int iter = 0; iter < iterations; ++iter)
{
int pair = iter % s_pairsCount;
JacobiRotation jrot = new JacobiRotation(s_pairs[pair,0],s_pairs[pair,1],matrix);
matrix = jrot.LeftRightMultiply(matrix);
eigen = jrot.RightMultiply(eigen);
}
// That was it as far as finding eigenvectors
int evec1,evec2;
FindSmallestTwoDiagonal(matrix, out evec1, out evec2);
// The eigenvectors corresponding to the two smallest eigenvalues are columns evec1 &
// evec2. These, in homogeneous space, are two different points on our line. We are
// going to convert them to an affine point & vector.
ColumnsToAffinePointVector(eigen, evec1, evec2, out origin, out direction);
}